All the reported experiments were performed using Epimod, a tool recently developed by our group to provide a generalframework to draw and analyze epidemiological systems. For more details regarding the workflow of analysis see SIR, where it is exploited the SIR model as a simple step by step guide of the package.
Folders:
Fig.1) SEIRS model and surveillance data on Piedmont region.
In Figure 1 is showed:
The population of the age class \(i\) is partitioned in the following seven compartments: (\(S_i\)), (\(E_i\)), (\(I_{ui}\)), (\(I_{qi}\)), (\(I_{hi}\)), (\(R_i\)), (\(D_i\)). With respect to the classical SEIRS model, we have added a transition from \(I_{ui}\) to \({I_{qi}}\) to model the possibility to identify undetected cases and isolate them. In this way an individual in \(I_{ui}\) tested as positive to the SARS-CoV-2 swab will be moved in the quarantine regime, \(I_{qi}\).
A detailed description of the model (e.g., system of ordinary differential equations, parameters, etc) is reported in the Supplementary Material.
The calibration phase was performed to fit the model outcomes with the surveillance Piedmont infection and death data (from February 24st to May 2nd) using squared error estimator via trajectory matching. Hence, a global optimization algorithm, based on (Yang Xiang et al. 2012), was exploited to estimate 13 model parameters characterized by a high uncertainty due to their difficulty of being empirically measured:
Consistently, Figure 2A and 2B show that the calibrated model is able to mimic consistently the observed infected and death cases (red line respectively). In Figure 3 the infected individuals for each age class are shown.
Fig.2)
Fig.3)
Three scenarios are implemented. In the the model is calibrated to fit the surveillance data (yellow). In the the model extends the second restriction beyond March, \(21^{st}\) without implementing the third restriction (blue). In the the model consider a higher population compliance to the third governmental restriction (green).
Fig.4) Stochastic simulation results reported as traces (on the left) and as density distributions (on the right).
The daily evolution of infected individuals is shown varying on the columns the the efficacy of individual-level measures and on the rows the efficacy of community surveillance.
Fig.5)
Fig.6)
Specifically, in Figure 6 we show the daily forecasts of the number of infected individuals with the efficacy of individual-level measures ranging from \(0\%\) to \(60\%\) on the columns (increasing by steps of \(20\%\)) and, on the rows, increasing capability (from 0% to 30%, by 10% steps) of identifying otherwise undetected infected individuals. These results are obtained as median value of 5000 traces for each scenario obtained from the stochastic simulation.
Pernice, S., M. Pennisi, G. Romano, A. Maglione, S. Cutrupi, F. Pappalardo, G. Balbo, M. Beccuti, F. Cordero, and R. A. Calogero. 2019. “A Computational Approach Based on the Colored Petri Net Formalism for Studying Multiple Sclerosis.” BMC Bioinformatics.
Yang Xiang, Sylvain Gubian, Brian Suomela, and Julia Hoeng. 2012. “Generalized Simulated Annealing for Efficient Global Optimization: The GenSA Package for R.” The R Journal. http://journal.r-project.org/.